Engaging devices of this type are generally used in modern motor vehicle gearboxes. The inwardly inclined surface portions of the tooth flanks are designed to increase the engaging force of the engaging sleeves, i.e. prevent an engaged gear from "popping out" due to the engaging sleeve being displaced from its engaged position under high torque load and during power shifting. The inwardly inclined surface of the tooth flank causes the force acting on the flank in the rotational direction to have a force component acting in the engagement direction of the engaging sleeve, the magnitude of the force component depending on the angle of the inclined surface portion relative to the rest of the flank surface.
One result of the engaging teeth of the engaging sleeve and the free gear being provided with tooth flanks, the outer end portions of which are inclined inwards, is that there must be, depending on the angle of incline, a certain amount of play between the engaging teeth of the engaging sleeve and the free gear. This play causers backlash in the gearbox and in modem gearboxes this backlash amounts to about 50% of the total backlash in the gearbox.
In general, the smaller the play is between the teeth of the engaging sleeve and the free gear, the smaller the risk will be for gear disengagement during power shifting. In modern serial production of gearboxes most units would function without any risk of disengagement even with a very small angle of inclination (between 1.degree. and 2.degree.) and consequently with very, little play, but it is unavoidable that for a small number of gear-boxes the variations within the tolerances will be such that there will be a large backlash in the gearbox despite the small angle of inclination of the flank portion, giving rise to the risk of gear disengagement. In order to achieve full security by unfavourable variation within tolerances in new gearboxes and in gearboxes with backlash caused by wear, the teeth of the engaging sleeve and the free gear are therefore made with surface portions, the angle of inclination of which is between 3.degree. and 4.degree.. However, the consequence of this is that the backlash in most gearboxes will be greater than what it actually needs to be.